Leslie Matrix

The Leslie matrix is a deterministic model of age-structured population dynamics, introduced by Patrick Leslie (1945). It projects population size and structure forward in time using age-specific fertility and survival rates. A Leslie matrix encodes these vital rates in a square matrix; multiplying the matrix by a population vector yields the population's composition at the next time step. This approach enables calculation of the population's asymptotic growth rate (λ), identification of stable age structure, and sensitivity analysis—understanding which vital rates most strongly influence population growth.